%0 Journal Article
%T On the dimension of the kernel of the linearized thermistor operator
%A Giovanni Cimatti
%J Electronic Journal of Differential Equations
%D 2013
%I Texas State University
%X The elliptic system of partial differential equations of the thermistor problem is linearized to obtain the system $$displaylines{ ablacdot(sigma(ar u) ablaPhi+sigma'(ar u)U ablaarvarphi)=0 quad ext{in }Omega,quad Phi=0quadhbox{on }Gammacr Delta U+sigma'(ar u)| ablaarvarphi|^2 U+2sigma(ar u) ablaar varphi cdot ablaPhi=0quad hbox{in }Omega, quad U=0quadhbox{on } Gamma. }$$ We study the existence of nontrivial solutions for this linear boundary-value problem, which is useful in the study of the thermistor problem.
%K Elliptic system
%K thermistor problem
%K existence
%K uniqueness of solutions
%U http://ejde.math.txstate.edu/Volumes/2013/38/abstr.html